I have a quick question. Why would it be a useless setup? It really just depends on use, which no one has addressed. A short, wide tire like a 31 x 12.50 might be ideal in sand, where floatation is more important than ground clearance. You would get the width advantage a 33 or 35 without the need for a gear change or a monster lift.
Pro - Comp, Mickey Thompson, and Interco have wide 31's with widths from 11.00 to 15.50. BFG makes a a/t and m/t 325/60, which is basically the same size as a 31x 12.50. The smallest rim recommended is a 15x9 for the BFG's.
They might be OK for street use with a little lift, but they will most likely rub sometimes. How are they going to be used?
That's just my opinion, I could be wrong...